User:Nick Vuci/TonalityDiamond

WORK-IN-PROGRESS AS OF 07MAY2025

Tonality Diamond

The tonality diamond is a symetric organization of otonal and utonal chords based around a central note and bounded by an odd-limit. First formalized in the 7-odd-limit by Max F Meyer in 1929, they became central to the music and theories of Harry Partch, who built his tonal system around the 11-odd-limit tonality diamond. The principle has been used both conceptually (such as for target intervals of temperaments) and practically (such as for instrument layouts) in xenharmonics ever since.

How to make a tonality diamond

Making a tonality diamond involves a few simple steps:

1. Take the numbers of an odd-limit and arrange them along two axes. Note: although you can arrange the numbers ascending, they are commonly arranged as if they were in the same octave of the harmonic series. IE, instead of 2 3 5 7 9 11 (2:3:5:7:9:11), the 11-limit diamond arranges them 2 9 5 11 3 7 (8:9:10:11:12:14).
2. Using one row as the numerator and the other as the denominator, fill in the cells with the ratios they form.
3. Make sure the decimal form of the ratio is between 1 and 2. If it is not, double one of the numbers until it is. Currently you will have all the intervals, but most of them will not be rooted (ie the lowest note of the chord will not be the root of the chord, it will be the relevant 1/1 interval). So if you want to make all the rows

History

The tonality diamond